Receiver Signal to Noise Ratios for IPDA Lidars Using Sine-wave and Pulsed Laser Modulation and Direct Detections Xiaoli Sun and James B. Abshire NASA Goddard Space Flight Center Solar System Division, Code 694 Greenbelt, Maryland 2077, USA xiaoli.sun-@nasa.gov. Introduction Integrated path differential absorption (IPDA) lidar can be used to remotely measure the column density of gases in the path to a scattering target []. The total column gas molecular density can be derived from the ratio of the laser echo signal power with the laser wavelength on the gas absorption line (on-line) to that off the line (off-line). Both coherent detection and direct detection IPDA lidar have been used successfully in the past in horizontal path and airborne remote sensing measurements. However, for space based measurements, the signal propagation losses are often orders of magnitude higher and it is important to use the most efficient laser modulation and detection techniue to minimize the average laser power and the electrical power from the spacecraft. This paper gives an analysis the receiver signal to noise ratio (SNR) of several laser modulation and detection techniues versus the average received laser power under similar operation environments. Coherent detection [2] can give the best receiver performance when the local oscillator laser is relatively strong and the heterodyne mixing losses are negligible. Coherent detection has a high signal gain and a very narrow bandwidth for the background light and detector dark noise. However, coherent detection must maintain a high degree of coherence between the local oscillator laser and the received signal in both temporal and spatial modes. This often results in a high system complexity and low overall measurement efficiency. For measurements through atmosphere the coherence diameter of the received signal also limits the useful size of the receiver telescope. Direct detection IPDA lidars are simpler to build and have fewer constraints on the transmitter and receiver components. They can use much larger size photon-bucket type telescopes to reduce the demands on the laser transmitter. Here we consider the two most widely used direct detection IPDA lidar techniues. The first techniue uses two CW seeder lasers, one on-line and one offline that are intensity modulated by two different freuency sine-waves signals before being amplified by a common laser amplifier. The receiver uses narrowband amplitude demodulation, or lock-in, signal processing at the given laser modulation freuencies [3,4]. The laser transmitter operates in a uasi CW mode with the peak power eual to twice the average power. The on-line and off-line lasers can be transmitted at the same time without interference. Another direct detection techniue uses a low duty cycle pulsed laser modulation [5,6] with the laser wavelengths alternating between on-line and off-line on successive pulses. The receiver uses time resolved detection and can also provide simultaneous target range measurement. With a lower laser duty cycle it reuires a much higher peak laser power for the same average power. 2. IPDA Lidar Receivers A coherent IPDA lidar [7] uses CW lasers and generates the intermediate freuency sinusoidal signal at the receiver from the coherent interference of the signal laser and local oscillator laser. The received signal is linear to the electromagnetic field of the incident laser light. The receiver freuency response is a linear combination of freuency response of the optical bandpass filter before the detector and that of the electrical filter after the detector. The latter is much narrower and effectively set the receiver
bandwidth. As a result, coherent detection receiver can rejects almost all the background light and detector dark noise. The dominant noise source is the shot noise from the local oscillator laser. Figure shows a block diagram of a coherent IPDA lidar receiver. An IPDA lidar using pulsed modulation and a direct detection receiver can provide a range resolved gas absorption measurements and minimize the effects of background light by range gating. A block diagram of the receiver is shown in Figure 3. Figure 4 shows a comparison of the laser signal for the sinusoidal and pulsed modulation IPDA lidars. Figure 3. Block diagram of direct detection pulsed IPDA lidar. Figure. Simplified Block diagram of an IPDA lidar with a coherent receiver The sine-wave modulation approach modulates the laser intensity with a sinusoidal signal with 50% duty cycle. The receiver, shown in Figure 2, is similar to the coherent detection receiver but without the local oscillator laser. The received signal is linear to intensity (suare of the field) of the incident light. The overall freuency response is determined by the receiver electrical bandwidth but the magnitude of the noise is determined by the total incident optical power, which is proportional to the optical filter bandwidth. Neither the coherent nor sine-wave modulation approaches provides target range measurement and detect clouds. A separate laser ranging channel is needed to measure the path length. Figure 4. Laser modulation format for direct detection IPDA lidars. 3. Receiver SNR Theory 3.. Coherent IPDA Lidar The mean and the standard deviation of the received signal for coherent IPDA lidar can be written as [2] c det c c 2 det N P LO 2 P LO Figure 2. Block diagram of lock-in detection IPDA receiver for sinusoidal laser intensity modulated laser signal. where det is the detector uantum efficiency, is the photon energy, c is the coherent mixing efficiency, and is the average received signal power, P LO is the average local oscillator laser power, N =2 is the
number of wavelengths, / 2 Tint is the receiver electrical noise bandwidth, and is the receiver integration time. The receiver signal to noise ratio can be written as c c c c N det n sig N with n sig the average number of detected signal photons over the receiver integration time. Coherent detection can be efficient and reaches the uantum limit by a factor of the coherent mixing efficiency. 3.2. Sine-wave Modulation IPDA Lidar The mean and standard deviation of the signal at for a sine-wave modulation lock-in detection IPDA lidar can be expressed as, L 2 det L 2 det sin N P bg sin I dark 2 2 where <P bg > is the CW background power, I dark is the detector dark current, and is the electron charge. The receiver shot noise was derived from freuency domain [2]. The receiver SNR can be expressed as det 2 2 N det 3.3. Pulsed IPDA Lidar sin P bg sin I dark Assuming single photon detection, the mean and standard deviation of the received signal for a pulsed direct detection IPDA lidar can be expressed as p p s N s N det det pulsed pulsed P bg pw I dark pw where pw is the pulse width and s is the pulse rate. det T N SNR pulsed pulsed int det I pulsed dty P bg dark dty with dty pw the duty cycle of the signal pulses. Compare to the sine-wave modulation, pulsed modulation and detection reduces the effect of background light and detector dark noise by the pulse duty cycle. 4. Comparison of Calculated SNR Under ideal conditions when the background light and detector dark noise are zero, the ratio of the SNRs of the sine-wave modulation lock-in detection to that of the coherent detection becomes SNR pulse 2 2 N c c Sine-wave modulation lock-in detection gives a lower SNR than coherent detection because of the unipolar laser intensity modulation. One half the laser power is not used to convey information but to maintain a proper bias. On the other hand, photon counting pulse detection can reach the same SNR as the coherent detection, because, under ideal conditions, the receiver SNR is fundamentally limited by the number of detected signal photons but not the modulation formats and the signal processing techniues. The ratio of SNRs between the lock-in and pulsed direct detection at a given background
light and detector dark noise can be written as SNR pulsed 2 2 N det det det det dty P bg I dark 4 for N 2 (online &offline only) P bg I dark 4 times higher that of sine-wave modulation. It also shows that the pulsed modulation reuired roughly /6 the average laser power to achieve the same SNR compared to sine-wave modulation. The performance differences become larger at lower signal levels and for higher background. More details about the derivation and experiment will be described in the presentation. Unver zero background light and detector dark noise, the ratio of the average signal power to achieve the same SNR is given by pulsed P sig 2 2 N sin 6 for (N 2) 2 8N 5. Measurements of Direct Detection Receiver SNRs We conducted laboratory experiments to measure the SNRs for lock-in and pulsed direct detection under similar conditions. The current to a 060 nm laser diode was modulated by an arbitrary waveform generator, which modulated the laser s output power in either sine-wave or pulses. A near infrared photomultiplier was used as photon counting detector. For lock-in detection, an oscilloscope was used after the detector to record the analog waveforms into a PC for the signal processing. A set of bandpass filters were used before the oscilloscope to avoid aliasing. For pulsed detection a multichannel scaler was used as a time resolved histogrammer. Figure 5 shows the measurement results along with the calculations given in the previous section. The parameter values used in the experiments are also listed in Table. 6. Summary and Conclusions The measurements agreed well with theory for sine-wave and pulsed modulation. At high signal conditions, the performance was limited by signal shot noise. In this region for the same received power the pulsed SNR is Figure 5. Measurement of the receiver SNR for both pulse and lock-in detection (symbols) along with the theoretical calculations (lines). Table - Experiment Parameters: Laser: 060 nm laser diode, intensity modulated by arbitrary waveform modulator Detector: Hamamatsu H0330-75 PMT used in photon counting configuration Pulsed Modulation: Pulse width: sec, rectangular shape Pulse rate: 0 khz, alternating between on-line and off-line Receiver integration time: = 0.2 sec Sinewave Modulation Lock-in Detection: Sinewave freuency, on-line: 50 khz Sinewave freuency, off-line: 5 khz Anti alaising filter before oscilloscope: 0 khz bandpass Lowpass filter type: 9th order Bessel Lowpass filter bandwidth: 5 Hz 7. Acknowledgements This work was supported by NASA Earth Science Technology Office (ESTO) Instrument Incubator Program (IIP).
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